How many 3-digit natural numbers (without repetition of digits) are there such that each digit is odd and the number is divisible by 5?

24 men and 12 women can do a piece of work in 30 days. In how many days can 12 men and 24 women do the same piece of work?

15 x 14 x 13 x ... x 3 x 2 x 1 = $3^m \times n$ Where m and n are positive integers, then what is the maximum value of m?

The sum of three consecutive integers is equal to their product. How many such possibilities are there?

A man started from home at 14:30 hours and drove to village, arriving there when the village clock indicated 15:15 hours. After staying for 25 minutes, he drove back by a different route of length $1.25$ times the first route at a rate twice as fast reaching home at 16:00 hours. As compared to the clock at home, the village clock is

An Identity Card has the number ABCDEFG, not necessarily in that order, where each letter represents a distinct digit $(1, 2, 4, 5, 7, 8, 9 \text{ only})$. The number is divisible by 9. After deleting the first digit from the right, the resulting number is divisible by 6. After deleting two digits from the right of original number, the resulting number is divisible by 5. After deleting three digits from the right of original number, the resulting number is divisible by 4. After deleting four digits from the right of original number, the resulting number is divisible by 3. After deleting five digits from the right of original number, the resulting number is divisible by 2.

Which of the following is a possible value for the sum of the middle three digits of the number?